if term is empty by post type

I’m trying to display a list of custom posts by category from a shared custom taxonomy. This issue I am having is if a category is selected in an alternate custom taxonomy then it displays in my list even though it is empty/not used in the custom post that is being queried. I feel like I am really close to solving this but I just can get over the hump. Any help would be greatly appreciated.

<?php
// get all the categories from the database
$cats = get_terms('apprenticeship-type', array('post_type' => 'apprenticeship-res', 'hide_empty' => true, 'parent' => 0));
$i = 0;
// loop through the categries
foreach ($cats as $cat) {
// setup the cateogory ID
$cat_id= $cat->term_id;
// Make a header for the category
$i++;
?>
<div class="panel">
<h4 class="panel-title"><a class="collapsed" href="#apprenticeshipDocumentsCollapse<?php echo $i ?>"><?php echo $cat->name?></a></h4>
<div id="apprenticeshipDocumentsCollapse<?php echo $i ?>" class="panel-collapse collapse">
<div class="panel-body">
<?php
// create a custom wordpress query
$args = array(
	'post_type' => 'apprenticeship-res',
	'tax_query' => array(
		array(
		'taxonomy' => 'apprenticeship-type',
		'field' => 'slug',
		'terms' => ".$cat->name."
		)
	)
);
$query = query_posts($args);
// start the wordpress loop!
if (have_posts()) : while (have_posts()) : the_post(); ?>
<?php // create our link now that the post is setup ?>
<a href="<?php the_permalink();?>"><?php the_title(); ?></a>
<?php the_excerpt(); ?>
<?php echo '<hr/>'; ?>
<?php endwhile; endif; // done our wordpress loop. Will start again for each category ?>
<?php wp_reset_query(); ?>
</div>
</div>
</div>
<?php } // done the foreach statement ?>